GluCat is a set of templates for Clifford Algebra written by Paul Leopardi. See http://glucat.sourceforge.net/ for details. Paul has designed the templates to work with numeric types. Paul supplies two version of his code.

framed_multi uses an STL map to store each object.

matrix_multi uses a sparse matrix representation from the Matrix Template Library to store each object.

GluCat is intended for use in numerical analysis applications, such as solution of PDEs.
GluCat uses a fast real matrix representation for Clifford algebras.
See the paper "A generalized FFT for Clifford algebras", Bulletin of the Belgian Mathematical Society - Simon Stevin, Volume 11, Number 5, 2005, pp. 663-688, and the preprint at
http://www.maths.unsw.edu.au/applied/reports/2004/amr04_17.pdf